Yuji Ijiri’s Fairness Question in Accounting: A Deontological Game Theoretic Approach

Tae Wan Kim; Pierre Jinghong Liang; John Hooker

doi:10.1515/ael-2022-0070

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Yuji Ijiri’s Fairness Question in Accounting: A Deontological Game Theoretic Approach

Tae Wan Kim , Pierre Jinghong Liang and John Hooker

Published/Copyright: March 1, 2024

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From the journal Accounting, Economics, and Law: A Convivium

Abstract

We revisit the question initially raised by Yuji Ijiri about the notion of fairness in accounting. We argue that the fairness question was important then and remains relevant today. First we situate Ijiri’s question in relevant debates in the history of accounting thoughts and in contemporary debates. Then we develop a framework of fair flow of information for accounting practices. To do so, we draw upon deontological ethical theory and the generalization principle, in particular. We invite a counter-example from the game-theoretic phenomenon of signal jamming to challenge the generalization principle. By addressing the challenge, we further clarify the appropriate uses of the generalization principle.

Keywords: Yuji Ijiri; fairness; game theory; signal jamming; ethics

JEL Classification: A13; M4; B1

Corresponding author: Tae Wan Kim, Carnegie Mellon University Tepper School of Business, Pittsburgh, PA, USA, E-mail: twkim@andrew.cmu.edu

Appendix: The Economic Equilibrium of Signal Jamming

In this appendix, we sketch a simple economic model of “signal-jamming” to link the economic equilibrium behavior to the moral standards of generalization.

Our economic model is a variant of the original model of Stein (1989) Holmström (1999). We briefly sketch the economic model here. Suppose the choice before an accountant (or auditor) is to agree with (or to certify) a client’s report that contains a bias. To be concrete, we represent this choice-by-choice variable b ∈ Rwhere the report is represented by outcome variable y = x + b where x ∼ N ( x 0 , σ x 2 ) is interpreted as the real economic outcome. In this context, a choice of b = 0represents a “truthful” report with respect to x, while any non-zero bias b ¬ 0 represents a report not truthful. Suppose the accountant/auditor works for a client whose preference is to increase the market’s perception of variable x based on the report y in addition to the true economic outcome x. Assume that the accountant/auditor chooses the bias b on behalf of the client, the economic choice becomes choosing a b to maximize a weighted average of the perceived and actual economic outcome minus the cost of the bias, or,

θ E [ E M [ x | y ] ] + ( 1 − θ ) E [ x ] − C ( b )

where θ is relative weight placed on the market expectation, E ^M[x|y] denotes the market’s expectation of x given realized y (different from client’s expectation E[.]), and C(b) denotes the expected economic loss to the clients due biased report (such as litigation and rearranging economic activities to support or justify the biased report). Relating to the action plan given earlier, the economic model so far represents the choice problem: C ₁ is captured by the auditor sharing the employer’s preference and C ₂ is captured by the maximization problem. That is, as long as the solution the maximization problem above, denotedb ^*, is chosen by the accountant/auditor (i.e., A ₁ = {b = b ^*}, the economic model is consistent with {C ₁ ∧ C ₂ ⇒ A ₁}

Now we lay out the economic consequence of this economic choice in a market equilibrium where such a choice is anticipated by the market participants. Following the rational expectation invoked in modern game-theoretic economic models, we endow the market full economic rationality by imposing the following two conditions. First, E ^M[x|y] is based on a market’s conjecture of the reporting choice of the client: E M [ x | y ] = E M [ x | y = x + b ˆ ] and second, the conjecture is correct in equilibrium, that is b ˆ = b * . Assuming C ( b ) = k b 2 2 , t he only rational choice in equilibrium is.

b ˆ = b * = θ k

The ratio expression captures the tradeoff auditors face succinctly. The ratio’s numerator θ represents the magnitude of the marginal benefit of the auditor agreeing to a more biased report (y). All else equal, the higher the θ, the more bias the auditor would tolerate. The ratio’s denominator k represents the magnitude of the marginal cost of the auditor agreeing to a more biased report (y). All else equal, the higher the k, the less bias the auditor would agree to certify. In practice, the magnitude of and k would change across economic environments such as different industries and over time. For example, for firms at times when market perception its value really matters (a high θ) such as when an IPO or seasoned offering is pending, the model predicts that auditors may be pressured to certify more bias all else equal. Conversely, for firms at times when external governance forces are tightened (a higher k) such as more regulatory oversight, the model predicts that auditors may be less willing to certify high level of bias. Overall, this expression describe the manager/auditor’s desire to change market’s perception fully knowing that the market is fully rational including having already anticipate such bias in the report (y) it receives.

The surprise result is that the equilibrium choice is b ≠ 0 even if it is completely expected and ineffective. Here is a quick proof sketch. First, let’s solve the E ^M[x|y] part of the objective function. Since this is the market’s expectation, not the auditor’s expectation, the market is required to make a conjecture about what it thinks the bias auditor will choose. Denote this conjecture as a b ˆ . Under this conjecture E M [ x | y ] = y − b ˆ . That is, the market would simply take the report y and subtract b from it as the best-response. Now the auditor knows this best-response by the market and substitutes this expression into the manager’s objective function, we have θ E { y − b ˆ } + ( 1 − θ ) E { x } − C ( b ) . From the manager’s standpoint, bias b is a choice variable, not a conjecture, so the objective function becomes E { x + b − b ˆ } + ( 1 − θ ) E { x } − C ( b ) , yielding a solution of b * = θ k . To complete the proof, since the game structure and all parameters are common knowledge, the market’s rational equilibrium conjecture, b ˆ , should also be θ k ; thus, b ˆ = b * = θ k .The key to this surprising equilibrium is that in the maximization problem, the market conjecture is taken as a given (i.e., not affected by the actual bias choice). To see this more clearly, we can put the true conjecture back into the optimization problem: max b θ E [ E M [ x | y , b ˆ = θ k ] ] + ( 1 − θ ) E [ x ] − C ( b ) = θ ( b − θ k ) + E [ x ] − C ( b ) , yielding the same solution. To gain intuition yet another way, suppose the market believes the report is “honest”: b ˆ = 0 , it follows that it is not economically rational for the client/accountant/auditor to choose b ^* = 0, because it does not maximize the objective θ E M [ x | y , b ˆ = 0 ] + ( 1 − θ ) E [ x ] − C ( b ) = θ b + E [ x ] − C ( b ) .

Generally, it is unclear whether all investors are reasonably expected to be aware of specific detailed opportunities and constraints that allow the biases to be introduced into the report. A slight modification of the economic model of reporting bias is illustrative here: suppose the bias the client/accountant introduces contains some noise: b * = b ˆ = π + ϵ ˜ b where π is a known constant and ϵ ˜ b is a mean-zero random variable known to client/accountant but unobservable to the outsider market participants. In this case, each client/accountant would bias the report by b ^*, but since the market participants observe only the total report y = x + π + ϵ ˜ b and are thus able to infer the expected bias, π, not the true bias, ( π + ϵ ˜ b ) .^[17] In this more general case, the behavior of adding bias into the accounting report is undone by the market participants only to the extent of the expected bias,^[18] not fully as in the original model.

References

Alexander, J. 2012. Experimental Philosophy. Cambridge: Polity Press.Search in Google Scholar

Bayou, M. E., A. Reinstein, and P. F. Williams. 2011. “To Tell the Truth: A Discussion of Issues Concerning Truth and Ethics in Accounting.” Accounting, Organizations and Society 36: 109–24. https://doi.org/10.1016/j.aos.2011.02.001.Search in Google Scholar

Binmore, K. 2015. “Why All the Fuss? The Many Aspects of the Prisoner’s Dilemma.” In The Prisoner’s Dilemma, edited by M. Peterson, 67–34. New York: Cambridge University Press.10.1017/CBO9781107360174.002Search in Google Scholar

Binmore, K. 2020. “Rationality as Consistency.” In Crooked Thinking or Straight Talk?, 27–53. Cham: Springer.10.1007/978-3-030-39547-6_2Search in Google Scholar

Bolton, G. E., and A. Ockenfels. 2000. “ERC: A Theory of Equity, Reciprocity, and Competition.” The American Economic Review 90 (1): 166–93. https://doi.org/10.1257/aer.90.1.166.Search in Google Scholar

Catanach, A. H., and S. C. Rhoades-Catanach. 2010. “Teaching Ethics in the Accounting and Tax Curriculum Using Milgram’s Agentic Shift Theory.” Research on Professional Responsibility and Ethics in Accounting 14, 189–212.10.1108/S1574-0765(2010)0000014012Search in Google Scholar

Chambers, R. 1966. Accounting Evaluation and Economic Behavior. Englewood: Prentice-Hall, Inc.Search in Google Scholar

Charness, G., and M. Rabin. 2002. “Understanding Social Preferences with Simple Tests.” Quarterly Journal of Economics 117 (3): 817–69. https://doi.org/10.1162/003355302760193904.Search in Google Scholar

Cunningham, R. L. 1967. “Ethics and Game Theory: The Prisoner’s Dilemma.” In Papers on Non-Market Decision Making, 11–26.10.1007/BF01718649Search in Google Scholar

DeFond, M., and J. Zhang. 2014. “A Review of Archival Auditing Research.” Journal of Accounting and Economics 58: 275–326. https://doi.org/10.1016/j.jacceco.2014.09.002.Search in Google Scholar

DeFond, M. L., C. Lennox, and J. Zhang. 2018. “The Primacy of Fair Presentation: Evidence from Regulators and the Courts.” Accounting Horizons 32 (3): 91–100, https://doi.org/10.2308/acch-52075.Search in Google Scholar

Devine, Carl Thomas. 2004. “Responsibilities, Ethics, and Legitimacy.” In Accounting Theory: Essays by Carl Thomas Devine, Vol. 3, edited by Harvey Hendrickson, and Paul Williams, 1–15. NY: Routledge.Search in Google Scholar

Donagan, A. 1977. The Theory of Morality. Chicago: University of Chicago Press.10.7208/chicago/9780226228419.001.0001Search in Google Scholar

Duska, R. F., and B. S. Duska. 2018. Accounting Ethics. Hoboken, NJ: John Wiley & Sons.10.1002/9781394260270Search in Google Scholar

Dworkin, R. 1978. Taking Rights Seriously, 136. Cambridge, MA: Harvard University Press.Search in Google Scholar

Dye, R. A., and S. S. Sridhar. 2004. “Reliability-Relevance Trade-Offs and the Efficiency of Aggregation.” Journal of Accounting Research 42: 51–88. https://doi.org/10.1111/j.1475-679x.2004.00129.x.Search in Google Scholar

Fischer, D. 2023. “FASB to Practitioners: ‘Substance Over Form’ for Me But Not for Thee – An Apologia.” Accounting, Economics, and Law: A Convivium 13 (3): 403–6, https://doi.org/10.1515/ael-2022-0046.Search in Google Scholar

Fischer, D., O. Ellman, and S. Schochet. 2021. “The Decline of Substance over Form in Accounting.” Accounting, Economics, and Law: Convivium 1–18.10.1515/ael-2019-0052Search in Google Scholar

Fischer, P. E., and R. E. Verrecchia. 2000. “Reporting Bias.” The Accounting Review 75 (2): 229–45. https://doi.org/10.2308/accr.2000.75.2.229.Search in Google Scholar

Fleischman, G., S. Valentine, and D. Finn. 2010. “Moral Intensity, Ethical Reasoning, and Equitable Relief Judgments.” Research on Professional Responsibility and Ethics in Accounting 14, 79–112.10.1108/S1574-0765(2010)0000014008Search in Google Scholar

Friedland, J. H. 2004. “The Need for an Accounting Court Revisited: Supplementing SEC Accounting Enforcement Actions.” International Journal of Disclosure and Governance 1: 238–59. https://doi.org/10.1057/palgrave.jdg.2040028.Search in Google Scholar

Gangolly, J. S., and M. E. Hussein. 1996. “Generally Accepted Accounting Principles: Perspectives from Philosophy of Law.” Critical Perspectives on Accounting 7: 383–407. https://doi.org/10.1006/cpac.1996.0042.Search in Google Scholar

Glover, J. 2018. “Yuji Ijiri: On Accountability.” Accounting, Economics, and Law: A Convivium 8 (1): 1–4, https://doi.org/10.1515/ael-2018-0004.Search in Google Scholar

Guttman, I., O. Kadan, and E. Kandel. 2006. “A Rational Expectations Theory of Kinks in Financial Reporting.” The Accounting Review 81 (4): 811–48. https://doi.org/10.2308/accr.2006.81.4.811.Search in Google Scholar

Harris, N. G. 1987. “Fairness in Financial Reporting.” Journal of Applied Philosophy 4: 77–88. https://doi.org/10.1111/j.1468-5930.1987.tb00205.x.Search in Google Scholar

Holmström, B. 1999. “Managerial Incentive Problems: A Dynamic Perspective.” The Review of Economic Studies 66: 169–82. https://doi.org/10.1111/1467-937x.00083.Search in Google Scholar

Hooker, J. N., and T. W. Kim. 2018. “Toward Non-Intuition-Based Machine Ethics.” In Proceedings of the 1th AAAI/ACM Joint Conference on Artificial Intelligence, Ethics and Society.Search in Google Scholar

Ijiri, Y. 1967. The Foundations of Accounting Measurement: A Mathematical, Economic, and Behavioral Inquiry. Hoboken, NJ: Prentice-Hall.Search in Google Scholar

Ijiri, Y. 1975a. Theory of Accounting Measurement. American Accounting Association. https://books.google.com/books?id=-acrAAAAYAAJ.Search in Google Scholar

Ijiri, Y. 1975b. “The Accountant: Destined to Be Free.” In The Inaugural Address on the Occasion of Being Named the First Robert M. Trueblood Professor of Accounting and Economics, Graduate School of Industrial Administration, Carnegie-Mellon University.Search in Google Scholar

Ijiri, Y. 1983. “On the Accountability-Based Conceptual Framework of Accounting.” Journal of Accounting and Public Policy 2: 75–81. https://doi.org/10.1016/0278-4254(83)90001-7.Search in Google Scholar

Kant, I. 1785. Groundwork of the Metaphysics of Morals, in Practical Philosophy, Mary J. Gregor (trans., ed.) 1996. [Originally published in 1785.]. Cambridge, UK: Cambridge University Press.Search in Google Scholar

Kleinman, G., P. Strickland, and A. Anandarajan. 2016. “The Accounting Court: Some Speculations on Why Not?” Group Decision and Negotiation 25: 845–71. https://doi.org/10.1007/s10726-015-9456-4.Search in Google Scholar

Korsgaard, C. M. 1996. The Sources of Normativity. Cambridge: Cambridge University Press.10.1017/CBO9780511554476Search in Google Scholar

Littleton, A. C. 1953. Structure of Accounting Theory. Sarasota: American Accounting Association.Search in Google Scholar

Lucas, J. R. 1959. “Moralists and Gamesmen.” Philosophy 34: 1–11. https://doi.org/10.1017/s0031819100029673.Search in Google Scholar

Mattessich, R. 1977. Accounting and Analytical Methods: Measurement and Projection of Income and Wealth in the Micro-and Macro-Economy. Scholars Book Company.Search in Google Scholar

McCumber, J. 2005. Reshaping Reason: Toward a New Philosophy. Bloomington, IN: Indiana University Press.10.2979/5066.0Search in Google Scholar

Mintz, S. M. 2010. “Linking Virtue to Representational Faithfulness in Making Judgments in a Principles-Based Environment.” Research on Professional Responsibility and Ethics in Accounting 14, 113–36.10.1108/S1574-0765(2010)0000014009Search in Google Scholar

Mock, T. J. 1976. Measurement and Accounting Information Criteria. Sarasota: American Accounting Association.Search in Google Scholar

Moonitz, M. 1961. Basic Postulates of Accounting; Accounting Research Study No. 01. New York: American Institute of CPAs.Search in Google Scholar

O’Neill, O. 2014. Acting on Principle: An Essay on Kantian Ethics, 2nd ed. Cambridge: Cambridge University Press.10.1017/CBO9781139565097Search in Google Scholar

Palmrose, Z.-V., and W. R. Kinney. 2018. “Auditor and FASB Responsibilities for Representing Underlying Economics-What US Standards Actually Say.” Accounting Horizons 32 (3): 83–90, https://doi.org/10.2308/acch-52074.Search in Google Scholar

Parfit, D. 2011. On What Matters, I. New York: Oxford University Press.10.1093/acprof:osobl/9780199572809.001.0001Search in Google Scholar

Paton, W. A., and A. C. Littleton. 1940. An Introduction to Corporation Accounting Standards. Sarasota: American Accounting Association.Search in Google Scholar

Ravenscroft, S., and Paul F. Williams. 2009. “Making Imaginary Worlds Real: The Case of Expensing Employee Stock Options.” Accounting, Organizations and Society 34 (6–7): 770–86. https://doi.org/10.1016/j.aos.2008.12.001.Search in Google Scholar

Scott, D. R. 1941. “The Basis for Accounting Principles.” The Accounting Review 16 (4): 341–9.Search in Google Scholar

Spacek, L. 1958. “The Need for an Accounting Court.” The Accounting Review 33 (3): 368–79.Search in Google Scholar

Spacek, L. 1969. A Search for Fairness in Financial Reporting to the Public: Selected Addresses, 1 & 2. Chicago, IL: A. Andersen.Search in Google Scholar

Stein, J. C. 1989. “Efficient Capital Markets, Inefficient Firms: A Model of Myopic Corporate Behavior.” Quarterly Journal of Economics 104: 655–69. https://doi.org/10.2307/2937861.Search in Google Scholar

Stocken, P. C., and R. E. Verrecchia. 2004. “Financial Reporting System Choice and Disclosure Management.” The Accounting Review 79 (4): 1181–203. https://doi.org/10.2308/accr.2004.79.4.1181.Search in Google Scholar

Stuebs, M. T. 2010. “Moral Confrontation: An Essential Companion to Moral Imagination.” Research on Professional Responsibility and Ethics in Accounting 14, 57–78.10.1108/S1574-0765(2010)0000014007Search in Google Scholar

Sunder, S. 2005. “Minding Our Manners: Accounting as Social Norms.” The British Accounting Review 37: 367–87. https://doi.org/10.1016/j.bar.2005.08.007.Search in Google Scholar

Sunder, S. 2008. “Econometrics of Fair Values.” Accounting Horizons 22: 111–25. https://doi.org/10.2308/acch.2008.22.1.111.Search in Google Scholar

Sunder, S. 2010. ““True and Fair” as the Moral Compass of Financial Reporting.” Research on Professional and Ethics in Accounting 14, 3–11.10.1108/S1574-0765(2010)0000014004Search in Google Scholar

Watts, R. L., and J. L. Zimmerman. 1990. “Positive Accounting Theory: A Ten Year Perspective.” The Accounting Review 65 (1): 131–56.Search in Google Scholar

Williams, P. F. 1987. “The Legitimate Concern with Fairness.” Accounting, Organizations and Society 12: 169–89. https://doi.org/10.1016/0361-3682(87)90005-5.Search in Google Scholar

Williams, P. F. 2010. “The Focus of Professional Ethics: Ethical Professionals or Ethical Profession.” Research on Professional Responsibility and Ethics in Accounting 14, 15–35.10.1108/S1574-0765(2010)0000014005Search in Google Scholar

Williams, P. F. 2023. “The Decline of Substance over Form in Accounting: A Problematic Dichotomy.” Accounting, Economics, and Law: Convivium 13 (3): 391–402, https://doi.org/10.1515/ael-2021-0119.Search in Google Scholar

Zeff, S. A. 2007. “The Primacy of “Present Fairly” In the Auditor’s Report.” Accounting Perspectives 6: 1–20. https://doi.org/10.1506/e773-5521-86u6-l3m0.Search in Google Scholar

Received: 2022-10-11

Accepted: 2024-02-03

Published Online: 2024-03-01

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https://doi.org/10.1515/ael-2022-0070

Keywords for this article

Yuji Ijiri; fairness; game theory; signal jamming; ethics